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  • Letter
  • Open Access

Hydrodynamic origin of Korteweg stresses from shear-induced horizontal buoyancy

Prabakaran Rajamanickam*

  • *Contact author: prabakaran.rajamanickam@manchester.ac.uk
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Phys. Rev. E 114, L013102 – Published 27 July, 2026

DOI: https://doi.org/10.1103/vckp-dcmf

Abstract

A recent study [P. Rajamanickam, Q. J. Mech. Appl. Math. 78, hbaf007 (2025)] of non-Boussinesq fluids in narrow channels identified a novel shear-induced horizontal buoyancy force that emerges upon depth-averaging the Navier–Stokes equations. This Letter demonstrates that this force is formally equivalent to the divergence of a Korteweg stress tensor. Unlike classical Korteweg stresses, which are typically attributed to molecular-scale cohesive potentials or implemented through assumed constitutive relations, we show that this emergent stress arises purely from self-coupled transport where the internal Ostroumov flow is kinematically coupled to the local density gradient. We derive explicit expressions for the effective stress coefficients, revealing a fundamental dependence on the Prandtl number and Grashof number. This correspondence is contrasted with classical Taylor dispersion, where the absence of self-coupling yields only a uniaxial stress. Although derived within a narrow-channel framework, our results establish a general hydrodynamic template for how quadratic gradient stresses can emerge from subscale, self-coupled flows, such as Marangoni or active-matter flows, offering a continuous transport-driven alternative to molecular mechanisms.

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Phys. Rev. E 114, L013102– Published 27 July, 2026
  • Received 11 April 2026
  • Accepted 13 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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